Unwrap tapered cylinder without UV distortion at tip
In mesh edit mode, mark edges as seams (in the edge menu -> mark seam).  Wherever you have a seam the unwrap operator will unstitch the seam in the UV map and unfold accordingly.

How you pick edges to mark as seams is dependent on what you're unwrapping. In this case you'll want to select the vertical edges towards the tip then mark seam.



When you unwrap these  should end up like your version 3.